Of Pinklestia's suggestions, I think the two that have the most promise are Amethyst and JJ Thunder.
The former is a Lord of Order if I remember right, and while she's a Lion-O equivalent in some ways, it would be more apt to consider her a Billy Batson equivalent. She's the heir to the House of Amethyst on Gemworld, where the Homo Magi fled ages ago, but she was raised on Earth. On Earth, she's notably younger than she is on Gemworld because of the time differential between realms. The main problem with her is that she is, by necessity, something of a part timer given her commitments on Gemworld.
JJ Thunder, meanwhile, is the inheritor of the Thunderbolt. Theoretically, that means he was born the Seventh Son of a Seventh Son on the Hour, Minute, and Moment of Seven. He's theoretically mystically quite potent aside the Thunderbolt as a result. This got ignored a bit in some of his later appearances, but it's still how Johnny at least got his powers. The issue with the young Mister Thunder is that while he's theoretically very powerful, he's not got much in the way of wisdom or knowledge, which is what the League really needs.
In terms of someone with Magical Power and Magical Knowledge, we might look into Doctor Occult/Rose Psychic, Sargon the Sorcerer, or Ibis the Invincible. Depending on the time and general situation of the setting, any of them might have the mojo and the know how to hack it with the League. Technically speaking, Accomplished Perfect Physician should also count given the whole 'Multiple past lives of mystic knowledge' thing he's got going on, but he's more focused on healing, so I can see where he wouldn't actually fix the problem.